@DBActive
As you write, the mountains of the east are a couple million years older than those in the west. They've worn down in size.
Oh, much more than a "couple of million", is actually over a billion years ago (roughly 1.2 gy). And at one time it was the highest mountain range on the planet and still holds the record for the tallest. However, the last building period of that range was around 260 mya, so they have been eroding for a long time.
And a lot of the difference between the two US coasts is the geology. The East Coast is largely "dead", geologically speaking. Where as the West Coast is still highly active, with ocean crust still subducting under the continent, various types of faults still changing the landscape, and a lot of volcanic features that are still highly active.
And one simple example, other than glacial rebound the East has been subsiding for millions of years. Meanwhile, the West is still quite often undergoing uplift and raising in altitude. Which means the canyons in most cases are still getting deeper. One thing most have backwards is that rivers themselves do not "cut canyons", it is the ground rising that forces the river to start to cut. If there is no crustal uplift, the river does not cut a canyon but instead meanders over time. The depth of canyons like the Grand and Hell's is not a sign of how much the river cut, but by how much the land rose since the river formed.